Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Grain-boundary migration controls grain growth, which is important in material processing and synthesis. When a vertical grain boundary ends at a horizontal free surface, a groove forms at the tip to reduce the combined grain-boundary and surface energies. The groove affects the migration of the grain boundary, and its effect must be understood. This work studies grain-boundary grooving by capillarity-driven surface diffusion with asymmetric and strongly anisotropic surface energies. The surface energies are described by the delta-function facet model that holds for temperatures above the roughening temperature of the bicrystal. Since the asymmetric anisotropy does not introduce a length scale, the asymmetric groove still grows with time t as t(1/4). Thus, the nonlinear partial differential equation that governs grooving is reduced by a self-similar transformation to an ordinary differential equation, which is then solved numerically by shooting methods. We vary systematically the crystallographic orientations of the bicrystal and the normalized grain-boundary energy. We find that the self-similar groove profile is faceted and asymmetric for most bicrystals. However, a few asymmetric bicrystals can also yield smooth and symmetric grooves. Some bicrystals may even form ridges instead of grooves. We also find that the asymmetric surface energies tilt the grain-boundary tip sideways, which induces the grain boundary to migrate. We show that anisotropic groove profiles measured in SrTiO3 and Ni can be well fitted by our model. (c) 2006 American Institute of Physics.